Random sampling technique for ultra-fast computations of molecular opacities for exoplanet atmospheres

Opacities of molecules in exoplanet atmospheres rely on increasingly detailed line-lists for these molecules. The line lists available today contain for many species up to several billions of lines. Computation of the spectral line profile created by pressure and temperature broadening, the Voigt profile, of all of these lines is becoming a computational challenge. We aim to create a method to compute the Voigt profile in a way that automatically focusses the computation time into the strongest lines, while still maintaining the continuum contribution of the high number of weaker lines. Here, we outline a statistical line sampling technique that samples the Voigt profile quickly and with high accuracy. The number of samples is adjusted to the strength of the line and the local spectral line density. This automatically provides high accuracy line shapes for strong lines or lines that are spectrally isolated. The line sampling technique automatically preserves the integrated line opacity for all lines, thereby also providing the continuum opacity created by the large number of weak lines at very low computational cost. The line sampling technique is tested for accuracy when computing line spectra and correlated-k tables. Extremely fast computations (~3.5e5 lines per second per core on a standard current day desktop computer) with high accuracy (< 1 % almost everywhere) are obtained. A detailed recipe on how to perform the computations is given.